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Sequences
Math 4MM4A9: Students will use
sequences and series
EQ
• How do I find the terms of a sequence using explicit and recursive formulas?
Formulas
• With an explicit formula, the number of the term is used to generate the terms of the sequence.
• With a recursive formula, the previous term in the sequence is used to generate the next term
Vocabulary
• Sequence – an ordered list of numbers• Term – a number in a sequence
*A sequence can be infinite (never ending) or finite.
*Answers must be in brackets – { }
Examples 1-4
Assignment
• Pg. 696, 11-35 odd
Do Now
• Pg. 696, #’s 36-37• Keep your answers in fraction form
Pg. 696, 11-35 odd
11. {5, 9, 13, 17}13. {-5, -9, -13, -17}15. {4, 9, 14, 19}17. {4, 0, -4, -8}19. {3/2, 2, 5/2, 3}21. {12.42, 21.17, 29.92,
38.67}23. {1, 8, 27, 64}25. {-2, -8, -18, -32}
27. {2, 4, 6, 8, 10, 12}29. {-6, 15, -27, 57, -111,
225}31. {10; 51; 256; 1281;
6,406; 32,031}33. {8, 22, 64, 190, 568,
1702}35. {3.34, 6.348, 12.9656,
27.52432, 59.553504, 130.0177088}
Assignment
• Pg. 696, 10-34 even
Pg. 696, 10-34 even
10. {5, 7, 9, 11}12. {-1, -3, -5, -7}14. {8, 14, 20, 26}16. {-4, -11, -18, -25}18. {6, 10, 14, 18}20. {9/4, 5/2, 11/4, 3}22. {6.26, 10.02, 13.78,
17.54}24. {-1, 1, -1, 1}
26. {1, 4, 7, 10, 13, 16}28. {0, -4, -8, -12, -16, -20}30. {7, 29, 117, 469, 1877,
7509}32. {10, 31, 94, 283, 850,
2551}34. {-2.24, -0.488, 1.6144,
4.13728, 7.164736, 10.7976832}
Assignment
• Pg. 975, 11.1, 1-6• Worksheet, 11.1, 1-6
Pg. 975, 11.1, 1-6 / Worksheet pg. 68, 1-6
1. {5, 2, -1, -4, -7}2. {-8, -4, 0, 4, 8}3. {2, 8, 18, 32, 50}4. {1, 6, 11, 16, 21}5. {16, 10, 4, -2, -8}6. {3, 6, 12, 24, 48}
1. {2.5, 5, 7.5, 10, 12.5, 15}
2. {0, ½, 1, 3/2, 2, 5/2}3. {13, 16, 21, 28, 37, 48}4. {20, 70, 220, 670, 2020,
6070}5. {1, 101, 201, 301, 401,
501}6. {-5, -15, -45, -135,
-405, -1215}
11.1 Continued
• Summation Properties and Formulas• EQ: How do I evaluate the sum of a series
expressed in sigma notation?
Summation Properties
1. To define the summation of a one term expression multiply the coefficient by the summation of the variable.
2. To find the summation of an expression that contains more than one term, find the summation of each individual term.
Summation Formulas
• Identify the value of “n”, which is the top number in the sigma notation.
• To find the summation for a constant series, multiply “n” by the constant.
• To find the summation for a linear series, multiply “n” by (n+1) and divide by 2.
• To find the summation for a quadratic series, multiply “n” by (n+1) and by (2n+1) and divide by 6.
Examples
Assignment
• Pg 696, #’s 42-50 all
Do Now: Solve
52
1
3k
x
Pg. 696, 42-50 all
42. 1243. 4044. 3045. 2446. -3047. -50
48. 749. 55/350. -100/3
Assignment
• Pg. 975, 11.1 10-15• Worksheet, 11.1, 13-20
Pg. 975, 11.1, 10-15/wkbk pg. 68, 13-20
10. 25811. 3012. 13013. 10514. 13515. 34
13. 12614. 18515. 21016. -2417. 1018. 1432.519. 39720. 1911.4
Pg. 696-697, 51-74 all
• Omit # 71 and # 72
Pg. 696-697, 51-74 all (omit 71-72)
51. 5/252. 3253. -1554. 15455. 2356. 5257. 1258. 859. 8460. 84
61. 42 73. 6862. 32 74. 64563. 3964. 16565. 16466. -11467. 668. 19969. -88/2170. 698/15